Work

Twisted q‐Yangians and Sklyanin determinants

Year: 2025

Type: article

Abstract: ‐Yangians can be viewed both as quantum deformations of the loop algebras of upper triangular Lie algebras and deformations of the Yangian algebras. In this paper, we study the quantum affine algebra as a product of two copies of the ‐Yangian algebras. This viewpoint enables us to investigate the invariant theory of quantum affine algebras and their twisted versions. We introduce the twisted Sklyanin determinant for twisted quantum affine algebras and show that they generate central elements in the center. We also establish various identities for the Sklyanin determinants.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70114

Authors: Naihuan Jing, Jian Zhang

Institutions: North Carolina State University, Central China Normal University

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Simons Foundation, National Natural Science Foundation of China, Fundamental Research Funds for the Central Universities

Awards: G1408471380, G2309554695, G2994029063, G3038044687, G3118607810